The Eﬀects of Surfaces on the Aerodynamics and Acoustics ... · be used as a basic guide to...

The Effects of Surfaces on the Aerodynamics and

Acoustics of Jet Flows

Matthew J. Smith∗

National Institute of Aerospace, Hampton, Virginia 23681

Steven A. E. Miller†

NASA Langley Research Center, Hampton, Virginia 23681

Aircraft noise mitigation is an ongoing challenge for the aeronautics research community.In response to this challenge, low-noise aircraft concepts have been developed that exhibitsituations where the jet exhaust interacts with an airframe surface. Jet flows interactingwith nearby surfaces manifest a complex behavior in which acoustic and aerodynamic char-acteristics are altered. In this paper, the variation of the aerodynamics, acoustic source,and far-field acoustic intensity are examined as a large flat plate is positioned relative tothe nozzle exit. Steady Reynolds-Averaged Navier-Stokes solutions are examined to studythe aerodynamic changes in the field-variables and turbulence statistics. The mixing noisemodel of Tam and Auriault is used to predict the noise produced by the jet. To validateboth the aerodynamic and the noise prediction models, results are compared with Par-ticle Image Velocimetry (PIV) and free-field acoustic data respectively. The variation ofthe aerodynamic quantities and noise source are examined by comparing predictions fromvarious jet and flat plate configurations with an isolated jet. To quantify the propulsion air-frame aeroacoustic installation effects on the aerodynamic noise source, a non-dimensionalnumber is formed that contains the flow-conditions and airframe installation parameters.

Nomenclature

AbbreviationsCFD Computational Fluid DynamicsFUN3D Fully Unstructured Navier-Stokes Three-Dimensional SolverHWB Hybrid Wing BodyNPR Nozzle Pressure RatioOASPL Overall Sound Pressure LevelPAA Propulsion Airframe AeroacousticsPIV Particle Image VelocimetryPSD Power Spectral DensityRANS Reynolds-Averaged Navier-StokesSHJAR Small Hot Jet Acoustic RigSMC Small Metal ChevronSPL Sound Pressure LevelSST Shear Stress TransportTKE Turbulent Kinetic EnergyTTR Total Temperature RatioSymbolsA Empirical constantc Speed of soundc∞ Free-stream speed of sound

∗Graduate Research Assistant, Department of Aerospace and Ocean Engineering, Virginia Tech, AIAA Member.†Research Aerospace Engineer, Aeroacoustics Branch, NASA Langley Research Center, 2 N. Dryden St. MS 461, Hampton,

VA, 23681, USA, AIAA Member, [email protected]

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American Institute of Aeronautics and Astronautics

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19th AIAA/CEAS Aeroacoustics Conference

May 27-29, 2013, Berlin, Germany

AIAA 2013-2041

This material is declared a work of the U.S. Government and is not subject to copyright protection in the United States.

Aeroacoustics Conferences

cτ Empirical constant associated with turbulent time scalecl Empirical constant associated with turbulent length scaleD Nozzle exit diameterDj Fully expanded jet diameterks Turbulent kinetic energy associated with fine-scale mixing noisels Turbulent length scaleMa Acoustic Mach numberMd Design Mach numberMj Fully expanded Mach numberM∞ Free-stream Mach numberp Static pressurepa Acoustic pressurepj Fully expanded static pressurepo Stagnation pressureqs Statistical source termSt Strouhal numberS Spectral density of acoustic pressureT0 Stagnation temperatureTj Fully expanded static temperatureu Mean streamwise velocity componentuj Fully expanded jet velocityx = x(x, y, z) Vector observer positionxI Estimate of jet impingement locationxp Axial distance to the plate trailing edgey = y(x, y, z) Source vectoryp Radial distance from the plate to the jet centerlineδη Spreading angle of the jetǫ Dissipation of turbulent kinetic energyΓ Non-dimensional numberγ Ratio of specific heatsτs Turbulent time scaleω Radial frequencyψ Observer angle from the upstream axis

Introduction

Aircraft noise mitigation is an ongoing challenge for the aeronautics research community. Noise associatedissues such as acoustic fatigue, annoyance to the public, and hearing loss have led to increased efforts towardthe reduction of jet noise. Increased understanding of jet noise produced in various flow conditions allowsfor improved acoustic prediction models, that are essential for the development of new low-noise aircraftdesigns. In support of these aircraft designs, shielding techniques have been studied that involve airframestructures located near jet engines to minimize noise perceived by the observer on the ground (see for examplePapamoschou and Mayoral1 or Huang and Papamoschou2). Jet flows interacting with these nearby surfacesresult in complex scattered acoustic fields that are difficult to model.

Supersonic aircraft configurations, such as those developed by Welge et al.3,4 for the 2020 to 2035timeframe or by Morgenstern et al.5 for the 2035 timeframe and beyond, demonstrate complicated nozzleand engine placement designed to reduce sonic boom and jet noise. Advanced low bypass ratio engines,as shown by Sokhey and Kube-McDowell,6 can be integrated into the airframe while potentially reducingjet noise. These concepts could also exhibit situations where the jet exhaust interacts directly with anairframe surface resulting in additional noise sources and a complicated scattered field. New jet noiseprediction methodologies need to be developed to address these complicated configurations and advancednozzle designs.

Another advanced concept is the Hybrid Wing Body (HWB) aircraft that shields jet noise by placing theengines above the airframe. This effect is described by Thomas et al.7 and Czech et al.8 Several techniques

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have been developed to predict the scattered noise from the engine. Some of these techniques include theBoundary Element Method,2 the Equivalent Source Method used in NASA’s Fast Scattering Code,9 and theray tracing method.10 However, only a limited number of source models have been developed for use withscattering methodologies.

Jet surface interactions produce a change in the noise sources associated with the aerodynamics of thejet flow. There have been several studies that examined the aerodynamic effects of nearby and impingingsurfaces on jet flows. Donaldson and Snedeker11 and Lamont and Hunt12 showed that jets impinging onoblique and perpendicular surfaces significantly affect the turbulence and shock cell structure of supersonicjets. Studies involving jets not directly impinging on surfaces include those by Sawyer13 and Al-Qutub andBudair14 among others. Capturing the effect on the acoustic source due to the changes in the aerodynamiccharacteristics of the jet flow-field is essential for accurate prediction of jet noise. The effect of nearby surfaceson the aerodynamic flow-field is dependent on multiple parameters such as NPR, TTR, nozzle geometry, theboundary condition on the surface, and the position of the surface relative to the jet.

In this paper, the variation of the aerodynamics, acoustic source, and far-field acoustic intensity areexamined as a large flat plate is moved relative to the nozzle exit. Steady Reynolds-Averaged Navier-Stokes(RANS) solutions are found using realistic nozzle and flat plate geometries to study the aerodynamic changesin the field-variables and turbulence statistics. The semi-empirical fine-scale mixing noise model of Tam andAuriault15 is used to predict the noise produced by the jet. This model is also used to examine the integrandof the acoustic source that uses quantities obtained from the steady RANS solution as its argument. Tovalidate both the aerodynamic and the noise models, results are compared with Particle Image Velocimetry(PIV) and free-field acoustic data, respectively. The variation of the field-variables, turbulence statistics,and noise is examined by comparing predictions from various jet and plate configurations with an isolatedjet. Multiple jet operating conditions are also examined. A non-dimensional number is developed to quantifythe effect of the surface on the aerodynamic noise source based on the jet operating condition and surfacelocation.

In the following sections of this paper, a non-dimensional number is introduced to quantify the effect of theairframe on the aerodynamic source, and the associated parameters describing the jet condition and surfacelocation are defined. Next, the steady RANS model is presented and compared with the PIV data of Bridgesand Wernet.16 Solutions of the steady RANS model are shown for multiple jet and plate configurations.Following the steady RANS assessment, a statistical noise prediction approach is described and comparedwith measurements of Bridges and Brown.17 Then, noise predictions of the isolated jet are compared tothe jet with a flat plate at various positions. Finally, a conclusion of this study and related future work arediscussed.

Analysis

The method by which a jet engine is integrated with the airframe of a flight vehicle can have significanteffect on the aerodynamic source of sound. This is a highly complicated problem that has received significantattention.7,8, 18 It is characterized by a large number of parameters that are highly interdependent. A non-dimensional number is formed, which has arguments involving the flow-conditions and jet position, that canbe used as a basic guide to ascertain whether the aerodynamic source is affected by the airframe relative tothe equivalent isolated jet aerodynamic source.

The coordinate system and geometry are illustrated in Fig. 1. Coordinates x, y, and z are normalized bythe nozzle diameter. This normalized coordinate system is used to illustrate results in the following sections.The origin of the coordinate system used for the analysis is located at the nozzle exit. The positive x axispoints in the jet principal direction, the y axis is normal to the plate, and the z axis is parallel to the plate.The plate is located at multiple cross-stream distances from the jet centerline axis to the plate surface, yp,and multiple streamwise distances from the nozzle exit to the trailing edge, xp.

Parameters are identified that have a direct impact on the aerodynamic source of the jet based on theposition of the airframe surface. These parameters are illustrated in Fig. 1. The first parameter is the fullyexpanded diameter of the jet,

Dj = D

√

Md

Mj

(

1 + γ−12 M2

j

1 + γ−12 M2

d

)(γ+1)/4(γ−1)

, (1)

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where D is the nozzle exit diameter, Dj represents the necessary equivalent nozzle exit diameter for a shockfree flow, Md and Mj represent the design Mach number and the fully expanded Mach number, respectively,and γ is the ratio of specific heats.

Additionally, xp is the distance from the nozzle exit to the trailing edge of the airframea parallel to thejet centerline. yp is the characteristic length from the nozzle centerline to the nearest airframe surface. xIis the shadow distance on the airframe surface from the nearest airframe surface point at which the jet firstinteracts with the airframe. This value is dependent on the problem geometry, the engine cycle condition,and xI = f(xI). The simplest estimate for xI is the jet impingement location, that is a function of the initialspreading rate of the jet. Here xI is approximated as,

xI =yp −D/2

tan[δη], (2)

where δη is the spreading angle of the jet. Values of δη are not readily available without numerical calculationsor measurement. Here, we adopt an empirical model developed by Lau19 for δη,

δη = 0.177(1− 0.294M2j )

(

1 +1

2(M2

j − 1)(Tj/To − 1.4)2)

, (3)

which is valid for a wide range of single-stream jet Mach numbers and temperature ratios. The flows ofthis investigation fall within the range of validity of Eqn. 3. Equation 3 is dependent on a wide range ofparameters that do not explicitly appear. Using these parameters a non-dimensional number is proposed,

Γ =

(

Dj

yp

)(

xpxI

)

. (4)

Alternatively, Eqn. 4 can be written as,

Γ =Djxp tan[δη]

yp(yp −D/2), (5)

where yp > D/2. Physically, Eqn. 5 is the ratio of the product of the jet and airframe length scales dividedby the cross-stream length scale and interaction distance. Small values of Γ can suggest that airframe effectson the jet aerodynamic noise sources are negligible. Likewise, large values of Γ can suggest that the effectsof the airframe on the aerodynamic noise sources of the jet are very large. In the following sections, Eqn. 5is evaluated using different jet conditions and airframe surface positions, and compared with numericalpredictions of the variation of the noise from the aerodynamic source.

Results

Steady RANS Assessment

The steady RANS equations are solved with a Computational Fluid Dynamics (CFD) approach using theNASA Fully Unstructured Navier-Stokes three-dimensional20 (FUN3D) solver. The Menter21 Shear StressTransport (SST) turbulence model is used to close the RANS equations. The model utilizes the strengthsof the Jones and Launder k-ǫ model22 and the Wilcox k-ω model.23,24 It utilizes the k-ω model in the innerregion of the boundary layer and switches to the k-ǫ model in the outer region and in free shear layers. Themodel also takes into account the transport of the principal turbulent shear stress within adverse pressuregradients. In this work, the noise source is dependent upon quantities obtained from the steady RANSsolution.

The plate positions relative to the nozzle exit assessed in this paper are shown in Table 1. The firstcolumn contains normalized streamwise distances from the nozzle exit to the edge of the flat plate and thesecond column shows normalized radial distances to the flat plate. Table 2 provides information regardingthe jet operating conditions analyzed. The operating conditions include three subsonic jets, one of which isheated, and two cold supersonic jets, one of which is over-expanded and the other ideally-expanded.

The field variables and turbulent statistics are discretized on a mixed element (structured-unstructured)computational grid. An unstructured grid is used to resolve the jet flow when the plate is present while a

aWe elect to use airframe and flat plate interchangeably in terms of the analysis.

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structured grid is retained to resolve the jet plume. All calculations are fully three-dimensional and utilizesymmetry. The nozzle geometries and flow conditions coincide with the PIV experiment of Bridges andWernet.16 Figure 2 shows an outline of the three-dimensional computational domain with the plate locatedtwo nozzle diameters, D, offset from the jet axis and parallel to the jet centerline. Values of po and To arespecified by boundary conditions consisting of nozzle pressure and temperature ratios at the nozzle inletand static pressure at the domain exit. A symmetric boundary condition is enforced on the x-y plane atz = 0. All other boundaries are defined with a free-stream condition of M∞ = 0.01 and ambient pressure.The SMC000 nozzle profile and a portion of the computational domain are shown in Fig. 3. This portion ofthe domain represents a slice in the x-y plane at z = 0 normalized by D. The full computational domainextends 75D downstream, 50D cross-stream along the z axis, and 100D cross-stream along the y axis toform a rectangular prism. The number of grid points in the domain with a plate present is 2,195,937 andthe number of elements is 2,827,906. The number of grid points in the domain without a plate present is1,180,575 and the number of elements is 1,472,843. These represent typical values for the cases examined.

Validation of the isolated jet steady RANS solution is performed by comparing the streamwise velocitycomponent and Turbulent Kinetic Energy (TKE) with the PIV data from the isolated jet experiment ofBridges and Wernet.16 The PIV dataset of Bridges and Wernet16 was developed in part to support thevalidation of jet noise prediction methodologies and steady RANS solutions for a wide range of jet velocitiesand temperatures. Mean velocities, TKE, and Reynolds stresses are important parameters for statisticalacoustic analogies. The first two are used for validation and subsequent analysis in this study.

The first comparison of steady RANS solutions with measurement is performed with a subsonic cold jetoperating at Mj = 0.513 from the convergent SMC000 nozzle. Contour plots of Fig. 4 show a qualitativecomparison of the streamwise velocity component and TKE. The velocity and TKE are normalized by thefully expanded velocity and its square, respectively. The steady RANS solutions are shown on the top halfplanes and the corresponding PIV data are shown on the bottom half planes. The streamwise velocity shownin Fig. 4(a) has noticeable variation from the PIV. The predicted thickness of the potential core past 6Dis below measurement and the fall-off past 8D is higher. The predicted peak TKE occurs near 5.5D andthe PIV peak TKE occurs further downstream at 6.25D. Furthermore, the predicted magnitude of peakTKE is lower than measurement. However, the global qualitative agreement is favorable compared to othersolutions produced by similar CFD codes (for example see Georgiadis et al.25).

Qualitative comparisons are conducted for the isolated jet by examining aerodynamic data along thecenterline and axial locations at x/D = 1, 4, and 16. Figure 5 shows the centerline variation of the normalizedstreamwise velocity component and TKE of both the steady RANS solution and PIV data. Figure 6 showsradial profile comparisons of the same quantities. Figure 5(a) shows that the predicted jet potential corelength is larger than measurement by 2D. The predicted streamwise velocity component follows the same≈ 1/x decay as the measured data along the centerline, shown in Fig. 5(a), and also matches the radialdecay at x/D = 1 and x/D = 4, shown in Fig. 6(a). The predicted TKE along the centerline matches theexperiment in terms of peak magnitude but the peak occurs one diameter further upstream than experiment.The peak magnitudes of TKE at x/D = 1 and x/D = 4 are larger than measurement by 0.0015 and 0.001TKE/Uj

2 respectively and are located 0.25D closer to the centerline than experiment. The solution under-predicts both the streamwise velocity component and TKE relative to measurement far downstream fromthe nozzle exit.

Qualitative comparisons are also conducted for the supersonic over-expanded jet operating at Mj = 1.29from the Md = 1.5 SMC016 nozzle. Again, the aerodynamic data is examined along the centerline andradial locations at x/D = 1, 4, and 16. Figure 7 shows the centerline variation of the normalized streamwisevelocity component and TKE of both the steady RANS solution and PIV data. Figure 8 shows radial profilecomparisons of the same quantities. As seen in Fig. 7, the predicted potential core length is 2D larger relativeto measurement. Within the potential core, the predicted shock cell structure locations compare favorablywith the experiment. The steady RANS solution over-predicts the rate of decay along the centerline shownin Fig. 7(a) and matches the radial decay in the potential core region at x/D = 1 and 4 as shown in Fig. 8(a).The steady RANS solution under-predicts the radial decay through the shear layer greater than 0.5D fromthe centerline. In the fully developed region of the flow at x/D = 16, the steady RANS solution only slightlyover-predicts the radial velocity profile. This is a favorable prediction relative to the TKE profile at x/D = 16shown in Fig. 8(b) and the subsonic jet predictions shown at x/D = 16 in Fig. 6. On the centerline thepeak TKE/Uj

2 is 0.03 below measurement and occurs 2D further downstream than measurement as shownin Fig. 7(b). The TKE predictions match the experiment in peak magnitude at x/D = 4 but over-predicts

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TKE/Uj2 at x/D = 1 and x/D = 16 by 0.015 and 0.005, respectively. In concurrence with the subsonic cold

jet comparisons of Fig. 6(b), the predicted TKE is lower than measurement further downstream from thenozzle. These trends are representative of all jet conditions shown in Table 2. The predictions are favorablerelative to experiment, for all jets examined, in the potential core region of the flow-field where inviscid termsdominate the equations of motion.

The steady RANS solutions of a Mj = 0.513 and TTR = 1.00 jet from the convergent SMC000 nozzlein the presence of a flat plate are now compared with the isolated jet operating at the same conditions.Figure 9 shows radial profiles of TKE at x/D = 10 for multiple plate positions. The plate is located atyp/D = −1,−2,−4,−6,−8, and −10 perpendicular to the jet centerline and extends to xp/D = 10 and20 downstream from the nozzle exit. Figure 9 shows that as the plate is moved closer to the jet the TKEdistribution is increasingly deformed. The peak magnitude closest to the plate decreases and the peakmagnitude furthest from the plate increases. This trend is amplified when increasing the xp/D location from10 to 20 for most of the cases examined. Furthermore, the jet plume is being deformed and is drawn towardthe plate due to a coanda like effect. For example, in Fig. 9(a) the xp/D = 10 and isolated jet case bothhave a TKE local minimum at y/D = 0. However, as the plate is moved closer as in Fig. 9(f) the localminimum of TKE for xp/D = 10 is now located at y/D = −0.16. The effect of extending the plate fromxp/D = 10 to xp/D = 20 amplifies the effect of the deformation of the jet plume as can be seen in Fig. 9(a).The peak TKE close to the plate is lower by 0.0005 TKE/Uj

2, and the peak TKE furthest from the plateis higher by 0.001 TKE/Uj

2. Similar changes of the TKE distribution are observed with all jet conditionsexamined. These preliminary numerical results show the changes in the aerodynamic characteristics of thejet plume induced by nearby surfaces. These changes affect the noise source amplitude and position as theplate location is altered.

Aeroacoustic Assessment

The results of the aerodynamic assessment show that nearby solid surfaces change the aerodynamic charac-teristics of the jet flow-field, even if the jet centerline is multiple diameters away from a solid surface. Toassess the changes of the acoustic source quantitatively, a statistical noise prediction approach is selected.Here, we choose the semi-empirical fine-scale mixing noise model of Tam and Auriault.15 The expression forthe spectral density of the acoustic pressure in the far-field, S, is given by,

S(x, ω) = 4π( π

ln 2

)3/2∫

∞

−∞

∫

∞

−∞

∫

∞

−∞

q2s l3s

c2τs

|pa(x;y, ω)|2 exp

[

−ω2l2

s

u24 ln 2

]

1 + ω2τ2s

(

1− uc∞

cos θ)2 dy (6)

where A is a constant coefficient, c is the speed of sound, u is the mean streamwise velocity component, xis the observer position, y is the source position, and ω is the radial frequency. qs = (4/9)A2c2ρ2k2s is astatistical source term where ks is the TKE associated with turbulence that produces fine-scale mixing noise.ks is set equal to the TKE computed from the steady RANS solution.

If predictions are restricted to the sideline direction and it is assumed that sound refraction by the jetshear layer has negligible effect on S, then a simplified form of pa(x;y, ω) can be constructed. As shown byMorris and Farassat26 the adjoint acoustic pressure at ψ = π/2 (the jet sideline) is,

|pa(x2;y, ω)|2 =

ω2

64π4c4∞x2

(7)

This approach does not take into account propagation effects associated with sound waves interacting withsurfaces such as the flat plate. This is advantageous because the effects of surfaces on the jet noise sourceare isolated.

The scales of turbulence in Eqn. 6 are related to the steady RANS solution of the jet by simple dimensional

models. The length scale is ls = clk3/2s /ǫ and the time scale is τs = cτks/ǫ, where ǫ is the dissipation of

TKE. The quantity, ǫ, is computed from the steady RANS solution as ǫ = 0.09ksω. By relating the turbulentscales to the steady RANS solution, the predicted noise is dependent on the jet mean flow. The mean flowis dependent on the boundary conditions, the nozzle geometry, and the position of the plate relative to thejet. The acoustic source strength and spatial distribution as a function of frequency is directly connected tothe steady RANS solutions.

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The coefficients A, cl, and cτ of Eqn. 6 are specified by comparing prediction with measurement, followingthe methodology of Tam and Auriault.15 The coefficients are calibrated with the SMC000 nozzle operatingat Mj = 1.00 and TTR = 1.00. The coefficients are constant irrespective of observer position, jet operatingcondition, or airframe geometry after calibration. The values are A = 3548.0, cl = 0.018, and cτ = 0.015, thatvary from those calculated by Tam and Auriault15 because the steady RANS solver and turbulence modeldiffer. Figure 10 shows the prediction compared with the experiment of Bridges and Brown.17 The SoundPressure Level (SPL) per unit St is represented on the y-axis, where St = ωDj/uj is the Strouhal number.The prediction captures the peak intensity and the nearly correct decay of intensity at high frequency. Thereis a slight discrepancy at lower frequencies where the decay of intensity is lower than measurement.

The effect that the flat plate has on acoustic intensity originating from the jet aerodynamic source isinvestigated by using the steady RANS solutions and Eqn. 6. The isolated jet predictions are subtracted fromthe installed jet predictions on a Power Spectral Density (PSD) basis for comparison. The first comparisonconsists of the cold subsonic jet at Mj = 0.513 and is presented in Fig. 11. In Fig. 11(a), the plate islocated at yp/D = −1,−2,−4,−6,−8, and −10 from the jet centerline and extends xp/D = 10 downstreamof the nozzle exit. In Fig. 11(b), the plate is located at yp/D = −1 from the jet centerline and extendsxp/D = 4, 10, and 20 downstream of the nozzle exit. When the plate is extended to xp/D = 10 downstreamof the nozzle exit, the results from Fig. 11(a) show only a small effect on the noise spectrum as the plateapproaches the centerline until the plate is at yp/D = −2. The noise deviation from the isolated jet reaches amaximum of −1.5dB at the lowest frequency and 0.75dB at the highest frequency when the plate is locatedat yp/D = −2. For all plate locations further than 2D away from the centerline, the noise deviations arewithin ±0.75dB from the isolated jet case. When the plate is located at yp/D = −1, the noise intensity is−6.9dB relative to the isolated jet case at the lowest frequency. The effect of varying the plate length relativeto the nozzle exit is displayed in Fig. 11(b). At the lowest frequency, the noise intensity deviation from theisolated jet reaches a maximum of −6.5dB, −6.9dB, and −7.9dB as the plate is extended to xp/D = 4, 10,and 20 downstream from the nozzle exit, respectively. At the highest frequency, the maximum deviation foreach plate extension does not exceed 0.75dB.

Predictions of the over-expanded supersonicMj = 1.29 jet from the convergent-divergent SMC016 nozzleare compared at various plate positions relative to the isolated jet. Figure 12(a) displays the effects of thesurface as it approaches the jet centerline, and Fig. 12(b) shows the effects of the surface as the plate length isextended relative to the nozzle exit. In Fig. 12(a), the noise intensity deviation from the isolated jet reaches amaximum of −1.0dB at the lowest frequency and 0.1dB at the highest frequency when the plate is located atyp/D = −2. For all plate locations further than 2D away from the centerline, the noise deviations are within−0.6dB from the isolated jet case at the lowest frequency and −0.02dB at the highest frequency. Whenthe plate is located at yp/D = −1, the noise reaches a maximum −6.4dB difference from the isolated jetcase. From Fig. 12(b), the noise deviation from the isolated jet reaches a maximum of −5.7dB, −6.4dB, and−7.7dB at the lowest frequency as the plate extends xp/D = 4, 10, and 20 downstream from the nozzle exit,respectively. The maximum dB difference from the isolated jet for each plate position is slightly decreasedin magnitude at lower frequencies when compared to the subsonic jet. There is no increase in noise intensityat high frequencies in contrast to the subsonic case.

Fig. 13 shows comparisons of an on-design Mj = 1.5 cold jet. From Fig. 13(a), the noise intensitydeviation from the isolated jet reaches a maximum of −1.0dB at the lowest frequency and 0.1dB at thehighest frequency when the plate is located at yp/D = −2 and xp/D = 10. For all plate locations furtherthan 2D from the centerline, the noise deviations are within −0.6dB from the isolated jet case at the lowestfrequency and −0.02dB at the highest frequency. When the plate is located at yp/D = −1, the noise reachesa maximum −6.4dB difference from the isolated jet case at the lowest frequency. In Fig. 13(b), the noisedeviation from the isolated jet reaches a maximum of −6.1dB, −6.4dB, and −8.1dB as the plate extendsto xp/D = 4, 10, and 20 from the nozzle exit, respectively. In regards to the magnitude of the maximumdifference and general trend of the spectra, the predictions of the jet and plate cases relative to the isolatedjet case are in close agreement with the over-expanded jet. In Fig. 13(b), there is a 0.4dB increase inmagnitude of noise intensity deviation with the plate located at yp/D = −1 and extending xp/D = 4 and20 downstream when compared to the over-expanded jet in Fig. 12(b) at lower frequencies. At the higherfrequencies there is no notable difference from the over-expanded jet.

The comparisons described above are representative of the other jet conditions analyzed in this study. Asthe jet approaches the plate there is a consistently larger difference in the noise spectrum from the isolatedjet at lower frequencies. This is due to the surface having a larger effect on the flow further downstream

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from the nozzle exit. It has been shown by Brooks et al.27 and Podboy28 that peak noise sources are locatednear the nozzle exit at higher frequencies and lower frequency peak noise sources are located multiple nozzlediameters downstream. The presence of the plate has a larger effect on the jet flow multiple diameters fromthe nozzle exit and therefore has a larger effect on the aerodynamic source at lower frequencies.

Next, the effect that the plate has on the acoustic source localization is examined by comparing noisesource maps of the jet flow for various plate positions using the steady RANS solutions and the integrandof Eqn. 6 near the peak frequency. Contours of SPL per unit St for the cold subsonic Mj = 0.513 jetat a frequency of 1kHz (St ≈ 0.3) are shown in Fig. 14. In this comparison the plate length extends toxp/D = 10 and the plate is located at yp/D = −10,−6,−4,−2, and −1 from the jet centerline. When theplate is located at yp/D = −10 in Fig. 14(a), the noise source distribution is unaffected by the presence ofthe plate. The two peak noise sources are located 9.5D downstream from the nozzle exit and are symmetricin magnitude about the jet centerline. There is no significant deformation of the source distribution dueto the presence of the plate further than 2D from the jet centerline. As the plate approaches the jet atyp/D = −2 shown in Fig. 14(d), the peak magnitude of the source closest to the plate is decreased by ≈ 1dBand the location is unchanged. When the plate is located at yp/D = −1, shown in Fig. 14(e), the peak noisesource furthest from the plate is decreased in magnitude by ≈ 1dB and is shifted 0.5D upstream relativeto the yp/D = −10 case shown in Fig. 14(a). The peak noise source distribution closest to the plate issignificantly deformed. The peak magnitude is decreased by ≈ 6dB and is shifted 1D upstream relative tothe yp/D = −10 case. An additional strong noise source is also formed close to the plate further downstreamat x/D = 14. This is a distinguishable difference from the other comparisons and could be explained by anobserved increase in TKE past the trailing edge of the plate. Figure 14 shows that the magnitude of thepeak acoustic source closest to the plate decreases as the plate surface approaches the jet centerline, and themagnitude of the peak acoustic source furthest from the plate is not significantly altered until the plate islocated at yp/D = −1 from the jet centerline. The location of the peak noise sources are unaltered until theplate is located at yp/D = −1. These comparisons represent trends that are consistent for all jet conditionsanalyzed.

Overall, the results show that the plate has a larger effect on the acoustic source as it approaches thejet centerline and as the plate length extends further downstream. As the effective jet impingement area ofthe plate is increased, the acoustic intensity radiating from the jet decreases. This result does not accountfor additional sources produced by the jet interacting with the surface. To quantify the effect of a nearbysurface on the jet noise source, the non-dimensional number Γ is used, as described in Eqn. 5. The overallsound pressure level (OASPL) is predicted over a frequency range of 20Hz to 100kHz for all plate locationsand jet conditions described in Tables 1 and 2 using the steady RANS solutions and Eqn. 6 at ψ = π/2. Theinstalled jet predictions of OASPL are subtracted from the isolated jet predictions on a PSD basis. Figure 15shows the absolute value of ∆OASPL as a function of Γ. The physics of the jet flow and airframe interactiondictate the value of Γ, and the value of Γ expresses how large an effect the jet airframe interaction has onthe jet noise source. The data collapse shows a critical value of Γ ≈ 1. As the cross-stream length scalesyp(yp−D/2) decrease to the equivalent of the product of the jet and airframe length scales (Djxp tan[δη]), Γincreases from 0 to 1. In the region, 0 < Γ . 1, the cross-stream length scales are dominant and the physicalquantities of the aerodynamic flow are not sufficiently altered to have a significant effect on the jet noisesource. In Fig. 15, small values of Γ approaching ≈ 1 have ∆OASPL less than 0.5dB and are considerednegligible. As the jet spreading angle, fully expanded jet diameter, or surface length increases the productof the jet and airframe length scales surpasses the cross-stream length scales and Γ increases beyond unity.As a result of the dominance of the jet and airframe length scales in this region, 1 < Γ < ∞, the physicalquantities of the aerodynamic flow are sufficiently altered and have a large effect on the jet noise source. Asshown in Fig. 15, values of Γ > 1 result in a range of ∆OASPL from 2.0dB to 2.75dB. It is observed that∆OASPL increases as Γ increases.

Calculation of Γ can be a useful tool when performing propulsion airframe aeroacoustics (PAA) analysis.When analyzing the noise propagation for a jet airframe interaction corresponding to Γ << 1, the airframeis expected to have a negligible effect on the jet noise source. For instance, a supersonic on-design Mj = 1.5cold jet with an airframe surface located at xp/D = 20 and yp/D = 4 corresponds to Γ = 0.099 and ∆OASPL= 0.083dB in Fig. 15. Since Γ << 1 and there is a negligible difference in the free-field jet noise source, theisolated jet aerodynamic source model along with a tailored Green’s function can used for a prediction thatincludes propagation about the airframe. A Mj = 0.985 jet with an airframe surface located at xp/D = 4and yp/D = 1 corresponds to Γ = 5.063 and ∆OASPL = 2.47dB in Fig. 15. The large value of Γ results

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in a large difference from the free-stream noise prediction; therefore a separate aerodynamic source modelis required for further analysis. An isolated jet aerodynamic source model can be used for a PAA analysiswith small values of Γ. For large values of Γ, some noise reduction can be attributed to the change in the jetnoise source and not to shielding effects. Recent studies have investigated the effects of liners on propulsionairframe surfaces.18 The effectiveness of airframe liners is associated with the location of the airframe relativeto the jet flow. The implications of Γ could be useful in future PAA liner studies.

Γ can include additional terms involving multiple jet streams or account for the boundary layer thicknesson the airframe. An equivalent parameter for the fully expanded jet diameter and jet spreading angle canbe developed for a dual-stream jet. However, a new model would be required for the estimation of the jetspreading angle. Inclusion of boundary layer effects will increase the effect of the cross-stream length scales.The airframe boundary layer thickness can be subtracted from the cross-stream length scales. A model toestimate the boundary layer thickness would be required. The general effect of the airframe on the jet noisesource as a function of Γ is expected to be consistent for these cases but may have a different critical value.

Conclusion

This study is motivated by low-noise aircraft designs that exhibit situations where the jet exhaust interactswith an airframe surface and to develop an understanding of the effect of nearby surfaces on the aerodynamicnoise sources of jet flows. A simplified analysis is performed to examine the variation of the aerodynamics,acoustic source, and far-field acoustic intensity as a large flat plate is moved relative to the nozzle exit.Steady RANS solutions are found using laboratory nozzle and flat plate geometries to study the aerodynamicchanges in the field-variables and turbulence statistics. The semi-empirical fine-scale mixing noise model ofTam and Auriault is used to predict the noise produced by the jet and to examine the integrand of theacoustic source. The aerodynamic and noise prediction models are validated by comparing results with PIVand free-field acoustic data, respectively. The variation of the field-variables, turbulence statistics, and noiseare examined by comparing predictions from various plate configurations with an isolated jet. The analysisincludes multiple jet operating conditions.

Results of the aerodynamic assessment show that nearby solid surfaces change the aerodynamic char-acteristics of the jet flow-field, even if the jet centerline is multiple diameters away from a solid surface.The effect of the surface is amplified as it approaches the jet centerline and as the plate length extendsfurther downstream. The induced change in the aerodynamic flow-field is shown to have a direct effect onthe source of jet noise. The installed noise predictions relative to the isolated jet show that the acousticintensity originating from the jet aerodynamic source is decreased as the effective impingement surface areaof the plate is increased.

A non-dimensional number is developed to quantify the effect of the surface on the jet aerodynamic sourcebased on the jet condition and surface location parameters. The reference number Γ physically describes theratio of the product of the jet and airframe length scales over the cross-stream length scales. The evaluationof Γ over the range of surface locations and jet conditions yields a critical value of Γ ≈ 1. Small values ofΓ suggest that airframe effects on the jet flow are negligible. Large values of Γ imply that the effects of thesurface on the jet aerodynamic source are very large. This simple calculation of Γ can be used as a basicguide to determine if the aerodynamic source is affected by the airframe relative to the equivalent isolatedjet aerodynamic source. Additional terms can be included with Γ to capture additional physical effects.

Acknowledgments

The first author is thankful for the support and motivation from his academic advisor, Professor ChrisFuller. The authors are grateful for continuous support from the National Aeronautics and Space Admin-istration (NASA) Fundamental Aeronautics Program (FAP) High Speed Project (HSP). Part of this workis supported by NASA through the National Institute of Aerospace (NIA) cooperative agreement numberNNL09AA00A. Drs. James Bridges and Mark P. Wernet of the NASA Glenn Research Center are gratefullyacknowledged for use of their experimental data.

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References

1Papamoschou, D. and Mayoral, S., “Experiments on Shielding of Jet Noise by Airframe Surfaces,” 15th AIAA/CEASAeroacoustics Conference, Miami, Florida, 11 - 13 May, AIAA Paper 2009-3326 , 2009.

2Huang, C. and Papamoschou, D., “Numerical Study of Noise Shielding by Airframe Structures,” 14th AIAA/CEASAeroacoustics Conference, Vancouver, British Columbia Canada, 5 - 7 May, AIAA Paper 2008-2999 , 2008.

3Welge, H. R., Nelson, C., and Bonet, J., “Supersonic Vehicle Systems for the 2020 to 2035 Timeframe,” 28th AIAAApplied Aerodynamics Conference, Chicago, Illinois, June 28 - July 1, AIAA Paper 2010-4930 , 2010.

4Welge, H. R., Bonet, J., Magee, T., Chen, D., Hollowell, S., Kutzmann, A., Mortlock, A., Stengle, J., Nelson, C.,Adamson, E., Baughcum, S., Britt, R. T., Miller, G., and Tai, J., “N+2 Supersonic Concept Development and SystemsIntegration,” NASA/CR 2010-216842 , 2010.

5Morgenstern, J. M., Stelmach, M., and Jha, P. D., “Advanced Concept Studies for Supersonic Commercial TransportsEntering Service in 2030-35 (N+3),” 28th AIAA Applied Aerodynamics Conference, Chicago, Illinois, June 28 - July 1, AIAAPaper 2010-5144 , 2010.

6Sokhey, J. S. and Kube-McDowell, M., “Low Noise Highly Variable Cycle Nozzle for Next Generation Supersonic Aircraft,”NASA ARMD Fundamental Aeronautics Program Technical Conference, 2008.

7Thomas, R. H., Burley, C. L., and Olson, E. D., “Hybrid Wing Body Aircraft System Noise Assessment with PropulsionAirframe Aeroacoustic Experiments,” 16th AIAA/CEAS Aeroacoustics Conference, Stockholm, Sweden, 7 - 9 June, AIAAPaper 2010-3913 , 2010.

8Czech, M. J., Thomas, R. H., and Elkoby, R., “Propulsion Airframe Aeroacoustic Integration Effects for a Hybrid WingBody Aircraft Configuration,” 16th AIAA/CEAS Aeroacoustics Conference, Stockholm, Sweden, 7 - 9 June, AIAA Paper2010-3912 , 2010.

9Tinetti, A. F., Dunn, M. H., and Pope, S., “Fast Scattering Code (FSC) User’s Manual, Version 2.0,” NASA CR2006-214510 , Oct. 2006.

10Agarwal, A., Dowling, A. P., and Graham, W., “A Ray Tracing Approach to Calulate Acoustic Shielding by the SilentAircraft Airframe,” 12th AIAA/CEAS Aeroacoustics Conference, Cambridge, Massachussetts, 8 - 10 May, AIAA Paper 2006-2618 , 2006.

11Donaldson, C. D. and Snedeker, R. S., “A Study of Free Jet Impingement. Part 1. Mean Properties of Free and ImpingingJets,” Journal of Fluid Mechanics, Vol. 45, 1971, pp. 281–319.

12Lamont, P. J. and Hunt, B. L., “The Impingement of Underexpanded, Axisymmetric Jets on Perpendicular and InclinedFlat Plates,” Journal of Fluid Mechanics, Vol. 100, 1980, pp. 471–511.

13Sawyer, R. A., “Two-dimensional Reattaching Jet Flows Including the Effects of Curvature on Entrainment,” Journal ofFluid Mechanics, Vol. 17, 1963, pp. 481–498.

14Al-Qutub, A. M. and Budair, M. O., “Experiments on the Flow Over a Flat Surface Impinged by a Supersonic Jet,”31st AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, San Diego, California, 10 - 12 July, AIAA Paper1995-2935 , 1995.

15Tam, C. K. W. and Auriault, L., “Jet Mixing Noise from Fine-Scale Turbulence,” AIAA Journal , Vol. 37, No. 2, 1999,pp. 145–153.

16Bridges, J. and Wernet, M. P., “The NASA Subsonic Jet Particle Image Velocimetry (PIV) Dataset,” NASA/TM-2011-216807 , 2011.

17Bridges, J. and Brown, C. A., “Validation of the Small Hot Jet Acoustic Rig for Aeroacoustic Research,” 11thAIAA/CEAS Aeroacoustics Conference, Monterey, California, 23 - 25 May, AIAA Paper 2005-2846 , 2005.

18Thomas, R. H., Czech, M. J., and Doty, M. J., “High Bypass Ratio Jet Noise Reduction and Installation Effects IncludingShielding Effectiveness,” 51st AIAA Aerospace Sciences Meeting, Grapevine, Texas, 7 - 10 January, AIAA Paper 2013-0541 ,2013.

19Lau, J. C., “Effects of Exit Mach Number and Temperature on Mean-Flow and Turbulence Characteristics in RoundJets,” Journal of Fluid Mechanics, Vol. 105, 1981, pp. 193–218.

20“Fun3D Manual,” NASA Langley Research Center, Hampton, VA, Aug. 2012, http://fun3d.larc.nasa.gov/.21Menter, F. R., “Two-Equation Eddy-Viscosity Turbulence Models for Engineering Applications,” AIAA Journal , Vol. 32,

No. 8, 1994, pp. 1598–1605.22Jones, W. P. and Launder, B. E., “The Prediction of Laminarization with a Two-Equation Model of Turbulence,”

International Journal of Heat and Mass Transfer , Vol. 15, 1972, pp. 301–314.23Wilcox, D. C. and Traci, R. M., “A Complete Model of Turbulence,” 9th AIAA Fluid and Plasma Dynamics Conference,

San Diego, California, 14 - 16 July, AIAA Paper 1976-351 , 1976.24Wilcox, D. C., “A Half Century Historical Review of the k-ω Model,” 29th AIAA Aerospace Sciences Meeting, Reno,

Nevada, 7 - 10 January, AIAA Paper 1991-0615 , 1991.25Georgiadis, N., Yoder, D. A., and Engblom, W. A., “Evaluation of Modified Two-Equation Turbulence Models for Jet

Flow Predictions,” 44th AIAA Aerospace Sciences Meeting and Exhibit, AIAA 2006-490 , 2006.26Morris, P. J. and Farassat, F., “Acoustic Analogy and Alternative Theories for Jet Noise Prediction,” AIAA Journal ,

Vol. 40, No. 4, 2002, pp. 671–680.27Brooks, T. F., Humphreys, W. M., and Plassman, G. E., “DAMAS Processing for a Phased Array Study in the NASA

Langley Jet Noise Laboratory,” 16th AIAA/CEAS Aeroacoustics Conference, Stockholm, Sweden, 7 - 9 June, AIAA Paper2010-3780 , 2010.

28Podboy, G. G., “Jet-Surface Interaction Test: Phased Array Noise Source Localization Results,” Proceeding of the ASMETurbo Expo, Copenhagen, Denmark, June 14-18, GT2012-69801 , 2012.

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Tables

Table 1. Plate Locations

Axial Location of Trailing Edge (xp/D) Radial Location Relative to Jet Centerline (yp/D)

4 1,2,4,6,8,10

10 1,2,4,6,8,10

20 1,2,4,6,8,10

Table 2. Jet Operating Conditions

Nozzle Setpoint NPR TTR Ma Mj

SMC000 3 1.197 1.000 0.5 0.513

SMC000 7 1.861 1.000 0.9 0.985

SMC000 27 1.357 1.814 0.9 0.678

SMC016 11606 2.748 0.761 1.128 1.29

SMC016 11610 3.670 0.706 1.31 1.5

Figures

Airframe Surface

xp

yp

y

x

z

Jet Centerline

Lipline

xI

δη

Axisymmetric Nozzle D

yp-D/2

Figure 1. The coordinate system and distance parameters used throughout this study.

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X

Y

Z

Inlet Plate

Outlet(y-z plane)

Free Stream

Symmetry(y-x plane)

Figure 2. An outline of the computational domain used for the CFD calculations. The edges of the compu-tational domain are shown as black lines. The flow of the jet is in the positive x direction and the coordinatesystem is centered at the nozzle exit. The domain extends 75 nozzle diameters downstream, 100 diameters inthe y direction, and 50 diameters in the z direction. The types of boundaries are labeled.

x/D

y/D

-5 -4 -3 -2 -1 0 1 2 3-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

Figure 3. A portion of the computational domain on the x-y plane at z = 0 showing the structured/unstructuredgrid of the convergent nozzle and flat plate located 2D away from the centerline. The nozzle geometry matchesthe NASA Glenn Research Center SMC000 nozzle with an exit diameter of D = 0.0508 m. The coordinates arenormalized by the nozzle exit diameter.

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x/D

y/D

2 4 6 8 10 12 14 16 18

-1

0

1

U/Uj0.950.90.850.80.750.70.650.60.550.50.450.40.350.30.250.2

(a) Streamwise Component of Velocity

x/D

y/D

2 4 6 8 10 12 14 16 18

-1

0

1

TKE/Uj2

0.0280.0260.0240.0220.020.0180.0160.0140.0120.010.0080.0060.0040.002

(b) Turbulent Kinetic Energy

Figure 4. Contours of (a) the streamwise velocity component and (b) TKE of the steady RANS solution andPIV data from the experiment of Bridges and Wernet.16 The steady RANS solutions are shown on the tophalf planes and PIV data are shown on the bottom half planes. The streamwise velocity component and TKEare normalized by the fully expanded velocity and the square of the fully expanded velocity respectively. Thecoordinates are normalized by the nozzle exit diameter D = 0.0508 m. The jet operates at Mj = 0.513 andTTR = 1.00 from the convergent SMC000 nozzle.

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x/D

U/U

j

0 5 10 15 200

0.2

0.4

0.6

0.8

1

(a) V elocity

x/D

TK

E/U

j2

0 5 10 15 200

0.005

0.01

0.015

0.02

0.025

Fun3DPIV

(b) TKE

Figure 5. The (a) steady RANS streamwise velocity component and (b) TKE along the jet centerline (y/D = 0& z/D = 0) compared with PIV data from the experiment of Bridges and Wernet.16 The streamwise velocitycomponent and TKE are normalized by the fully expanded velocity and the square of the fully expandedvelocity respectively. The spatial coordinate is normalized by the nozzle exit diameter D = 0.0508 m. The jetoperates at Mj = 0.513 and TTR = 1.00 from the convergent SMC000 nozzle.

y/D

U/U

j

-1 -0.5 0 0.5 10

0.2

0.4

0.6

0.8

1

(a) V elocity

y/D

TK

E/U

j2

-1 -0.5 0 0.5 10

0.005

0.01

0.015

0.02

0.025

0.03

0.035

Fun3D x/D=1Fun3D x/D=4Fun3D x/D=16PIV x/D=1PIV x/D=4PIV x/D=16

(b) TKE

Figure 6. The (a) steady RANS streamwise velocity component and (b) TKE at x/D = 1, x/D = 4, andx/D = 16 compared with PIV data from the experiment of Bridges and Wernet.16 The velocity and TKE arenormalized by the fully expanded velocity and the square of the fully expanded velocity respectively. Thespatial coordinate is normalized by the nozzle exit diameter D = 0.0508 m. The jet operates at Mj = 0.513 andTTR = 1.00 from the convergent SMC000 nozzle.

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x/D

U/U

j

0 5 10 15 200

0.2

0.4

0.6

0.8

1

1.2

(a) V elocity

x/D

TK

E/U

j2

0 5 10 15 200

0.005

0.01

0.015

0.02

0.025

Fun3DPIV

(b) TKE

Figure 7. The (a) steady RANS streamwise velocity component and (b) TKE along the jet centerline (y/D = 0& z/D = 0) compared with PIV data from the experiment of Bridges and Wernet.16 The streamwise velocitycomponent and TKE are normalized by the fully expanded velocity and the square of the fully expandedvelocity respectively. The spatial coordinate is normalized by the nozzle exit diameter D = 0.0508 m. The jetoperates at Mj = 1.29 and TTR = 1.00 from the convergent-divergent SMC016 nozzle.

y/D

U/U

j

-1 -0.5 0 0.5 10

0.2

0.4

0.6

0.8

1

1.2

(a) V elocity

y/D

TK

E/U

j2

-1 -0.5 0 0.5 10

0.005

0.01

0.015

0.02

0.025

0.03

0.035

Fun3D x/D=1Fun3D x/D=4Fun3D x/D=16PIV x/D=1PIV x/D=4PIV x/D=16

(b) TKE

Figure 8. The (a) steady RANS streamwise velocity component and (b) TKE at x/D = 1, x/D = 4, andx/D = 16 compared with PIV data from the experiment of Bridges and Wernet.16 The velocity and TKE arenormalized by the fully expanded velocity and the square of the fully expanded velocity respectively. Thespatial coordinate is normalized by the nozzle exit diameter D = 0.0508 m. The jet operates at Mj = 1.29 andTTR = 1.00 from the convergent-divergent SMC016 nozzle.

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y/D

TK

E/U

j2

-1 -0.5 0 0.5 10.015

0.02

0.025

0.03Isolated Jetxp/D=10xp/D=20

(a) yp/D = −10

y/D

TK

E/U

j2

-1 -0.5 0 0.5 10.015

0.02

0.025


(b) yp/D = −8

y/D

TK

E/U

j2

-1 -0.5 0 0.5 10.015

0.02

0.025


(c) yp/D = −6

y/D

TK

E/U

j2

-1 -0.5 0 0.5 10.015

0.02

0.025


(d) yp/D = −4

y/D

TK

E/U

j2

-1 -0.5 0 0.5 10.015

0.02

0.025


(e) yp/D = −2

y/D

TK

E/U

j2

-1 -0.5 0 0.5 10.015

0.02

0.025


(f) yp/D = −1

Figure 9. Radial variation of TKE at x/D = 10 downstream of the nozzle exit. The spatial coordinate isnormalized by the nozzle exit diameter. Parts (a)-(f) show the steady RANS solution with the plate locatedat 10, 8, 6, 4, 2, and 1D from the jet centerline respectively and extending 10 and 20D downstream from thenozzle (D = 0.0508 m). The jet operates at Mj = 0.513 and TTR = 1.00 from the convergent SMC000 nozzle.

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St

SPL

per

uni

t St (

dB r

e 20

µ P

a)

10-2 10-1 100 101

75

80

85

90

95

100

105

110

SHJAR ExperimentPrediction

Figure 10. The free-field prediction at R/D = 100 and ψ = 90 degrees using the model of Tam and Auriault15

compared with the experiment of Bridges and Brown.17 The jet operates at Mj = 1.00 and TTR = 1.00 fromthe convergent SMC000 nozzle with D = 0.0508 m.

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St

∆SP

L p

er u

nit S

t (dB

re

20 µ

Pa)

10-2 10-1 100 101-8

-6

-4

-2

0

2

Isolated Jetyp/D = -10yp/D = -8yp/D = -6yp/D = -4yp/D = -2yp/D = -1

(a) xp/D = 10

St

∆SP

L p

er u

nit S

t (dB

re

20 µ

Pa)

10-2 10-1 100 101-8

-6

-4

-2

0

2

Isolated Jetxp/D = 4xp/D = 10xp/D = 20

(b) yp/D = −1

Figure 11. Attenuation plot of the free-field prediction at R/D = 100 and ψ = 90 degrees using the model ofTam and Auriault15 for the isolated jet and plate cases. For part (a), the plate is located at 1, 2, 4, 6, 8, and10D laterally from the jet centerline and extends 10D downstream from the nozzle. For part (b) the plate islocated at 1D laterally from the jet centerline and extends 4, 10, and 20D downstream from the nozzle. Thejet operates at Mj = 0.513 and TTR = 1.00 from the convergent SMC000 nozzle with D = 0.0508 m.

St

∆SP

L p

er u

nit S

t (dB

re

20 µ

Pa)

10-2 10-1 100 101-8

-6

-4

-2

0

2


(a) xp/D = 10

St

∆SP

L p

er u

nit S

t (dB

re

20 µ

Pa)

10-2 10-1 100 101-8

-6

-4

-2

0

2


(b) yp/D = −1


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St

∆SP

L p

er u

nit S

t (dB

re

20 µ

Pa)

10-2 10-1 100 101-8

-6

-4

-2

0

2


(a) xp/D = 10

St

∆SP

L p

er u

nit S

t (dB

re

20 µ

Pa)

10-2 10-1 100 101-8

-6

-4

-2

0

2


(b) yp/D = −1


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x/D

y/D

0 2 4 6 8 10 12 14 16 18 20-1

-0.5

0

0.5

1SPL per St

98979695949392919089

(a) yp/D = −10

x/D

y/D

0 2 4 6 8 10 12 14 16 18 20-1

-0.5

0

0.5

1SPL per St

98979695949392919089

(b) yp/D = −6

x/D

y/D

0 2 4 6 8 10 12 14 16 18 20-1

-0.5

0

0.5

1SPL per St

98979695949392919089

(c) yp/D = −4

x/D

y/D

0 2 4 6 8 10 12 14 16 18 20-1

-0.5

0

0.5

1SPL per St

98979695949392919089

(d) yp/D = −2

x/D

y/D

0 2 4 6 8 10 12 14 16 18 20-1

-0.5

0

0.5

1SPL per St

98979695949392919089

(e) yp/D = −1

Figure 14. Contours of peak acoustic source downstream from the nozzle exit at f = 1000Hz (St ≈ 0.3). Thespatial coordinates are normalized by the nozzle exit diameter. Parts (a)-(e) show the acoustic source with theplate located at yp/D = −10,−6,−4,−2, and −1 respectively and extending 10D downstream from the nozzle.The jet operates at Mj = 0.513 and TTR = 1.00 from the convergent SMC000 nozzle with D = 0.0508 m.

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Γ

∆O

ASP

L (

dB r

e 20

µ P

a)

10-2 10-1 100 101-0.5

0

0.5

1

1.5

2

2.5

3SP3SP7SP27SP11606SP11610

Figure 15. Results of ∆OASPL as a function of non-dimensional number Γ (Eqn. 5). ∆OASPL is calculatedrelative to the isolated jet case for each airframe configuration and jet condition as listed in Tables 1 and 2,respectively.

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The Eﬀects of Surfaces on the Aerodynamics and Acoustics ... · be used as a basic guide to...

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